Step 1: Recall the literacy rates from the 2011 Census for Union Territories.
Step 2: Compare the literacy rates of the given UTs. According to the 2011 Census:
Lakshadweep: 91.85%
Daman and Diu: 87.10%
Andaman and Nicobar Islands: 86.63%
Chandigarh: 86.05%
Step 3: Identify the highest. Lakshadweep had the highest literacy rate among all Union Territories.